ARLINGTON, Texas — Barry Church remembers Dallas coach Jason Garrett talking turnovers on the first day of training camp.

The Cowboys’ safety and his teammates showed they were listening in the season opener – and showed off their new defensive scheme, too.

Brandon Carr returned an interception 49 yards for the clinching touchdown, Church had another defensive score on a fumble, and the Cowboys beat Eli Manning and the New York Giants for the first time at their fancy $1.2 billion stadium with six takeaways in a 36-31 victory Sunday night.

“Coach Garrett showed us the first day of training camp what the percentages were,” said Church, who scooped a loose ball and ran 27 yards to the end zone in the third quarter. “If we could get turnovers, our chances of winning were greater.”

Dallas needed all six, though, because Manning threw for 450 yards and four touchdowns, including three to Victor Cruz. The Giants had the ball and were down just 30-24 in the final 2 minutes when Manning’s pass went off the hand of running back De’Rel Scott into Carr’s arms.

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The cornerback beat Manning down the sideline with 1:50 left on the last of Manning’s three interceptions.

Here are five things that helped dropped Manning to 4-1 for his career in Dallas owner Jerry Jones’ showplace:

1. IT’S A SCHEME AND AN ATTITUDE: The Cowboys had only 16 turnovers all last year, switched to a four-man front with new defensive coordinator Monte Kiffin and swore all preseason that taking the ball away was the foremost thing on their minds. They proved it from the first snap of the season.

DeMarcus Ware intercepted Manning’s first pass, and the Giants turned it over on their first three possessions. The Cowboys didn’t take advantage of the early gifts, but built a big enough lead to hold off a New York comeback once the Giants finally stopped turning it over.

It matched the most turnovers for the Giants since 1987, when they had seven against New Orleans. And it was the most Dallas has forced since 2003.

“Just tells you our system is so much built on attitude,” said defensive line coach Rod Marinelli, who was defensive coordinator for Chicago last year when the Bears led the NFL with 44 turnovers.

2. MANNING MYSTIQUE: After the Giants won the first NFL regular-season game at the Cowboys’ new stadium in 2009, Manning signed his name on a wall in the visitor’s locker room. Manning’s had some more signature moments, but now has his first loss in five games there even though he still had a chance to win after the first five turnovers.

The Giants were down 27-10 late in the third quarter before Manning threw the second TD to Cruz. The Giants then cut it to 30-24 on Cruz’s 10-yard TD with 8:54 left.

After an exchange of punts, New York was at its own 17 when Manning converted third-and-5 with a 26-yard pass to Rueben Randle, then came the game-clinching interception right after the 2-minute warning.

“You know there’s going to be mistakes and different things to fix every week,” Manning said. “You just hope that the mistakes aren’t costly ones.”

3. ROMO RIBS: Tony Romo missed Dallas’ final offensive play of the first half when he was hit in the ribs and had the wind knocked out after being crushed between Mathias Kiwanuka and Justin Trattou after throwing an incompletion. Kyle Orton came on to finish the half, but Romo was back after halftime.

Romo, who was 36 of 49 for 263 with two touchdowns and one interception, said his ribs affected him, and didn’t dismiss the notion that the injury could linger. But he said “no one really cares” if he’s hurt and that he wasn’t going to worry about X-rays until Monday. Romo played with broken ribs for several games in 2011.

“One tough player, one tough man,” Jones said. “He will go out and play in pain and play hurt.”

4. GOT TO HOLD ON: David Wilson has to start holding onto the football for the New York Giants. Wilson fumbled twice, one inside the Cowboys 10 on the Giants’ first running play of the game and the other returned 27 yards for a touchdown.

As a rookie last season, he fumbled on his second career carry. Asked if Wilson was still his starting running back, Coughlin responded, “I’m not going to answer that now. Give us a little time to work on these things. He’s very much in our thoughts – he’s got to play.”

Still, Coughlin was clear when he called the fumbles “demoralizing to the whole team” and says Wilson won’t play unless he can hold onto the ball.

5. WITTEN FINDS END ZONE AGAIN: Witten caught both of Romo’s scoring passes, and they were the only offensive touchdowns for the Cowboys. Witten had just three touchdowns last season while setting an NFL record for tight ends with 110 catches. He had eight catches for 70 yards against the Giants and became the third tight end in NFL history with 9,000 yards receiving.

“I had a bunch of catches (last year), but touchdowns were something we worked a lot on,” Witten said.